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Journal of the Optical Society of America B

Amplified spontaneous emission and maximum gain–length product revised for general line shapes

Riccardo Tommasini, Juerg E. Balmer

Published Apr 1, 1999• 12 citations
Publisher

Abstract

The theory of amplified spontaneous emission (ASE) and the gain–length product at saturation is revised. Formulas valid for both peak and integrated lines are given. In the latter case the solution for a general Voigt stimulated-emission line shape is presented, whereas in the two limiting cases of Gaussian and Lorentzian line shapes an approximation better than the one obtained by the steepest-descent method is successfully achieved. Various parameters that take into account the ratio of spontaneous to stimulated linewidths, the form factor depending on the linewidths of the inhomogeneous and homogeneous convoluted line shapes, and the population inversion fraction arise from the theory, giving the complete functional dependence for both the ASE photon flux and the gain–length product.

DOI
10.1364/josab.16.000538

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The theory of amplified spontaneous emission (ASE) and the gain–length product at saturation is revised. Formulas valid for both peak and integrated lines are given. In the latter case the solution for a general Voigt stimulated-emission line shape is presented, whereas in the two limiting cases of Gaussian and Lorentzian line shapes an approximation better than the one obtained by the steepest-descent method is successfully achieved. Various parameters that take into account the ratio of spontaneous to stimulated linewidths, the form factor depending on the linewidths of the inhomogeneous and homogeneous convoluted line shapes, and the population inversion fraction arise from the theory, giving the complete functional dependence for both the ASE photon flux and the gain–length product.
The output of pulsed, homogeneously broadened amplified spontaneous emission (ASE) lasers operating under conditions of strong saturation is considered. An expression for the maximum power (energy) per unit volume that may be extracted from steady-state (pulsed) systems is derived and shown to be independent of the saturation intensity. Numerical calculations of the temporal evolution of the populations in the laser levels and the growth in the ASE fluence, peak intensity, and spectral width are presented for three types of laser system: quasi steady state, short pump pulses, and self-termination. In all cases the growth in the fluence of the ASE pulse is found to agree with an analytic solution derived for conditions of strong saturation. The calculated growth in intensity of the ASE pulse is compared with expressions derived by Pert [J. Opt. Soc. Am. B11, 1425 (1994)] for the steady-state case. As expected, good agreement is found for the quasi-steady-state system, but in the limit of strong saturation significant differences occur for the short pump pulse and self-terminating laser systems considered. For all cases considered, the variation of the spectral width of the ASE pulse is found to be in reasonable agreement with that predicted by Pert for steady-state conditions.
A theory is described which accounts for the dependence of the spectral distribution of amplified spontaneous emission on the length and inversion density of the active medium. For an inhomogeneously broadened line an unanticipated dip occurs in the plot of linewidth against length at lengths slightly greater than the critical length, but is explained by a simple physical analysis. Agreement occurs between the theory and that of Yariv and Leite (1963) in the regime over which their theory is expected to work. Observations by other workers on the spectral distribution of amplified spontaneous emission systems are discussed.
Spectral line broadening due to resonance absorption and induced emission is investigated for general spectral distributions of the radiation field using the frequency-dependent relaxation operator method. An analytic self-consistent solution is found for the case of equal spectral profiles of field and radiative cross sections. The often-assumed Gaussian distribution of the field in saturated amplifiers is shown to yield symmetrical doublet structure for the radiative cross sections if the induced rates are larger than or comparable to the Gaussian width. A similar calculation was therefore performed for double Gaussian field spectra that reproduces such doublet structure for the cross sections in the case of narrowly spaced Gaussians. Self-consistent solutions of gain and line-broadening equations are accordingly expected to favor the sidebands, and at very high powers and gains amplified-spontaneous-emission lines should generally split into two lines of equal intensity separated by an averaged Rabi frequency. Since the cross-section profiles vary along the amplifier, the overall gain may be diminished, although the local cross sections have enhanced maxima at high powers.
The widely used technique for determining optical gain and absorption from single-pass, amplified spontaneous emission (ASE) is analyzed with particular attention given to active-volume saturation and three-dimensional effects. The results for homogeneously broadened media show that the population inversion and hence the gain in the active region is diminished by high levels of spontaneous and ASE. The externally measured gain is further reduced for large output collection apertures that admit incompletely amplified off-axis rays. Criteria are given for the excitation and detection geometries required to ensure accurate (∼10-percent) gain measurement. The simultaneous measurement of the equilibrium absorption coefficient can be made under less restrictive conditions.
Amplified spontaneous emission (ASE) occurs in media with large gain, and affects both the magnitude and the spatial distribution of the inversion. In this work we theoretically study the effect of ASE in three-dimensional, rectangular slab amplifiers, using Monte Carlo type computer simulations. We found that in one-dimensional amplifiers ASE is always larger at the edges so that the inversion has a maxima at the center of the amplifier. However, in two- and three-dimensional amplifiers, the inversion has a minimum at the center of the amplifier for low gain, and a maximum at the center of the amplifier for high gain. Thus, the inversion profile can be changed by increasing the gain from a minimum at the center, through a plateau, to a maximum at the center. A simple analytical theory was developed and agrees with these results.